To borrow a phrase from Robert Bauval, this falls under the Spooky Stuff category.
It is a very strange connection between the Grand Metre (1 + royal cubit), the base of the natural logarithm ⅇ, and the royal cubit as measured in inches.
2018-11-29: added Spooky Stuff 7 and 8
2018-12-03: added Spooky Stuff 9
2018-12-04: added Spooky Stuff 10
I have no explanation for this. It just highlights again the ancient origins of the metre, inch and royal cubit, and how they mysteriously link together with π and ⅇ. But what about φ you ask?…. here you go:
Questions for bonus marks:
For Spooky Stuff 10, it’s a bit more long-winded than the ones above, so need to post it in chunks.
We start with this equation as a good approximation for the Grand Metre, which is equal to 1 + the Royal Cubit:
Now if we consider this equation, similar to the above:
We can solve for x:
Now If we use
as a very close approximation for the English foot ( 0.3047197551 versus 0.3048 )
Which is the same as the solution for x above, to 4 decimal places.
gives us the Grand Metre which is 5 English feet, while the solution to
gives us 6 English feet.